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These are replies submitted by AntoineR

@mmcdara while it is indeed a transfer function, it's the controller's transfer function using the direct synthesis method (not sure about the translation, it's synthèse directe in french). The method works by having the desired form of the reaction of the system to the controller you want to have given, and the transfer function of the process given too, so your only unknown is the controller's transfer function.

Say you want a response of the form 1/(tau_c*s + 1), you would do something like this :

1/(tau_c*s+1) = (Gp*Gc)/(1 + Gp*Gc), where Gp is the process's transfer function and Gc is the controller's.


In the case of this exercice I had been given Gp = ( K*(-b*s + 1)) / (tau^2*s^2 + 2*x*tau*s + 1) and the desired form as (-b*s + 1) / (tau_c*s + 1), with a bit of algebra I obtained the function you can find higher.

Once solving the Gc equation, you get Gc = Kc(1 + 1/(tau_I * s) + tau_D*s), which is the transfer function of a PID controller!


I hope I could explain the context clearly! :)

@acer Thanks a lot for the help! I did indeed want to have A, B and C explicitly as for the context (designing a PID controller), those values are required explicitly!

I did something similar to what you did from what dharr had done using simply A:= coeff(...) and then B:=coeff(...)/A !

Thanks a bunch for both of you guys's time investment in this! I'll definitely use this little Maple Worksheet more often, and I've learnt about the importance of not just assuming Maple understands the multiplications!

@dharr awesome thank you so much for your help, it means a lot!

Have a great day :)



wow thank you so much! it's really appreciated! the script you sent works for me, but if I try to use the exact same function as you did I get the error message "Error, (in convert/parfrac) argument not a rational function", do you know why it would do that?

EDIT : I get the error, what I don't understand is how you obtained the form of the equation you have with seemingly the same input as mine!


Thanks again!

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